A New Lower Bound For A Ramsey-Type Problem

Let 3 ≤ r < s be fixed integers and let G be a graph on n vertices not containing a complete graph on s vertices. The main aim of this paper is to provide a new lower bound on the size of the maximum subset of G without a copy of complete graph K r . Our results substantially improve previous bounds of Krivelevich and Bollobás and Hind.

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Correspondence to Benny Sudakov*.

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* Research supported in part by NSF grants DMS-0106589, CCR-9987845 and by the State of New Jersey. Part of this research was done while visiting Microsoft Research.

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Sudakov*, B. A New Lower Bound For A Ramsey-Type Problem. Combinatorica 25, 487–498 (2005). https://doi.org/10.1007/s00493-005-0029-3

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Mathematics Subject Classification (2000):

  • 05C35
  • 05C55
  • 05D10